An Improved Estimation of Parameter of Morgenstern-Type Bivariate Exponential Distribution Using Ranked Set Sampling

In this chapter, the authors suggest some improved versions of estimators of Morgenstern type bivariate exponential distribution (MTBED) based on the observations made on the units of ranked set sampling (RSS) regarding the study variable Y, which is correlated with the auxiliary variable X, where (X,Y) follows a MTBED. In this chapter, they firstly suggested minimum mean squared error estimator for estimation of 𝜃2 based on censored ranked set sample and their special case; further, they have suggested minimum mean squared error estimator for best linear unbiased estimator of 𝜃2 based on censored ranked set sample and their special cases; they also suggested minimum mean squared error estimator for estimation of 𝜃2 based on unbalanced multistage ranked set sampling and their special cases. Efficiency comparisons are also made in this work.

Reliability assessment of the standby system with dependent components by bivariate exponential distributions

In the reliability analysis of systems, all system components are often assumed independent and failure of any component does not depend on any other component. One of the reasons for doing so is that considerations of calculation and elegance typically pull in simplicity. But in real-world applications, there are very complex systems with lots of subsystems and a choice of multiple components that may interact with each other. Therefore, components of the system can be affected by the occurrence of a failure in any of the components. The purpose of this paper is to give an explicit formula for the computation of the reliability of a system with two parallel active components and one spare component. It is assumed that parallel components are dependent and operate simultaneously. Two distributions of Freund’s bivariate exponential and Marshall–Olkin bivariate exponential are used to model dependency between components. The results show that the reliability of the system with Freund’s bivariate exponential distribution has lower reliability. The circumstances that lead to them, namely load-sharing in the case of Freund, results in lower reliability. Finally, a numerical example is solved to evaluate the proposed model and sensitivity analysis is performed on the system reliability function. The obtained results show that because the proposed model is influenced by the dependency, compared to traditional models, it has the characteristic of leading to reduced time to (first) failure for achieving specified reliability.

A Note on the Time to Failure of a Two-Unit Parallel Redundant System with Deterioration on a Lattice

In this paper, we consider a two-unit parallel redundant system with deterioration on a lattice, where each unit has multi-stage deterioration levels, say, n levels. The transition from one deterioration level to the subsequent level occurs following the well-known Marshall-Olkin bivariate exponential distribution. We derive the closed form of the Laplace transform of the time to system failure in the two-unit parallel redundant system with deterioration on n×n lattice without repair and simultaneous failure, as well as the simple system on 3×3 lattice.

Two Ways to Quantify Korean Drought Frequency: Partial Duration Series and Bivariate Exponential Distribution, and Application to Climate Change

Studies using drought index to examine return levels of drought can be classified into two approaches: univariate frequency analysis using annual series extracted from drought index time series and multivariate frequency analysis that simultaneously reflects various characteristics of drought. In the case of drought analysis, it is important to properly consider the duration, so, in this study, univariate frequency analysis is performed using the partial duration series. In addition, a bivariate frequency analysis is performed using a relatively simple bivariate exponential distribution to give a more realistic return level to major drought events in the past while reflecting the correlation between drought severities and durations. The drought severity–duration–frequency curves using each of the two frequency analyses are derived, and these curves are used to examine how the drought phenomenon currently in progress is evolving. From this, the advantages and disadvantages of the two approaches, as well as the points to be aware of in application, are discussed. Finally, using the two approaches to the proposed drought frequency analysis, the behavior of Korea’s future extreme droughts is investigated under the conditions of various future climate change scenarios.